Third. Diffie-Hellman Protocol

For the third asignament, we worked in group of three, in order to practice the Diffie-Hellsman Protocol, the  members name are Alice, one being Bob, and one Eve, and then changing roles so everyone gets to be Eve one time.

When my turn to be Eve came, Adriana was Alice, and Rodolfo was Bob. They talked in secret generating the values of p and g. Then they made said values, and their respectives X and Y public.:

• p = 13
• g = 5
• X = 12
• Y =8

With this then I have to start to obtain the values of x and y, and then the key. So I started first with obtaining x from the X function:

To get x, I took a way with every number lower than p and I got this value as seen here.  And this is the procedure that I made.

I just multiplied the current power of 5*5 again, and then divided by 13, to check the residue(module). 

Now, we can try the same with y, as we saw in the previous table, we already got your value which resulted in y = 3 and here to check the value.

And

K = (12^3) % 13 =  12*12*12 % 13 = 12

K =  (8^12) % 13= (8*8*8*8*8*8*8*8*8*8*8*8) % 13 = 12

I concluded that the Key was 12, with x = 6, and y = 3. Adriana and Rodolfo confirmed this.

As we saw in the previous table, we already got your value which resulted in y = 3.